Question: Multiply the following complex numbers: $({-1-3i}) \cdot ({-1+i})$
Solution: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-1-3i}) \cdot ({-1+i}) = $ $ ({-1} \cdot {-1}) + ({-1} \cdot {1}i) + ({-3}i \cdot {-1}) + ({-3}i \cdot {1}i) $ Then simplify the terms: $ (1) + (-1i) + (3i) + (-3 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ 1 + (-1 + 3)i - 3i^2 $ After we plug in $i^2 = -1$ , the result becomes $ 1 + (-1 + 3)i - (-3) $ The result is simplified: $ (1 + 3) + (2i) = 4+2i $